Abstract

Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of _positive property_. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes _positive property_ as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" _Pure attribution_ seems likely to be related to the Leibnizian concept of perfection. By a careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, _Gödel’s Ontological Argument_, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism and modal realism.